Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}-2x+8y &= 7 \\ 2x+3y &= -7\end{align*}$
Answer: We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $11y = 0$ Divide both sides by $11$ and reduce as necessary. $y = 0$ Substitute $0$ for $y$ in the top equation. $-2x+8( 0) = 7$ $-2x = 7$ $-2x = 7$ $x = -\dfrac{7}{2}$ The solution is $\enspace x = -\dfrac{7}{2}, \enspace y = 0$.